[Phys-L] routine assumptions and plausible hypotheses ... or not

[John Denker <jsd@av8n.com>]

On 07/08/2012 06:06 AM, Jeff Bigler wrote:
> Perhaps my engineering bias is showing, but why not explicitly teach
> students about making assumptions:
>
> 1. Which quantities are likely involved in a given problem?
>
> 2. What assumptions are usually good in the "real-life" situations most
> of us encounter on a day-to-day basis?
>
> 3. Which additional assumptions are we making in order to simplify the
> problem, even if they make the problem no longer representative of what
> happens in most "real-life" situations?
>
> 4. After calculating the desired quantity with the desired assumptions,
> how would changing certain of these assumptions affect the outcome?
>
> Then, on tests, ask students to explicitly state which assumptions
> they're making, and include questions that ask what would happen if
> certain assumptions were changed.

I understand that and mostly agree with it.  From the expert point of 
view, it makes sense.  

However, from the student point of view, the situation is not nearly
so cut-and-dried.  It's necessary but not sufficient for students to
hear what needs to be done.  The hard part is learning /how/ to do it.

There is a problem with item (2) in the list above.  The problem is 
that there are infinitely many assumptions that we make on a day-to-day
basis.  It takes experience and judgment to determine which assumptions
are worth questioning, or even worth mentioning.

To illustrate the sort of thing I mean, here is just the tippiest tip
of the iceberg.  In the introductory physics class:
 *) pulleys are frictionless (unless otherwise specified)
 *) strings are massless (unless otherwise specified)
 *) strings have negligible stretch but also negligible stiffness (u.o.s)
 *) when weighing things in air, buoyancy corrections are negligible (u.o.s)
 *) all velocities are small compared to the speed of light (u.o.s)
 *) length-scales, time-scales, and accuracies are such that spacetime can
  be considered locally flat.  In other words, no tidal stresses (u.o.s)
 *) the conventional g-vector (direction and magnitude) includes significant
  contributions from the centrifugal field associated with the earth's rotation.
 *) on the other hand, velocities and accuracies are such that Coriolis effects 
  are negligible (u.o.s)
 *) etc. etc. etc.

I emphasize that many of these assumptions are utterly nontrivial.  For example,
often we keep the terrestrial centrifugal terms but throw away the Coriolis terms.
There are reasons for that, but the reasons are non-obvious.  Similarly, when we
look at the energy-versus-velocity relationship,
 -- We keep the zeroth-order term, rest energy E0 = m c^2
 -- We keep the first-order term, momentum p = mv
 -- We keep the second-order term, kinetic energy KE = 1/2 m v^2
 -- We throw away the third-order term and all higher terms.

How do you justify keeping the first three terms and throwing away all the rest?
There are reasons for this, but the reasons are non-obvious.

This is related to one of the fundamental rules for how to make decisions (in
science, in business, et cetera).  The rule is to consider all the /plausible/
hypotheses.  You cannot possibly consider all hypotheses without restriction.
Alas it takes judgment, intuition, and common sense to decide what's plausible
and what's not.

It's necessary but not sufficient to tell students this needs to be done.
The hard part is teaching them /how/ to do it.